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Quantum Information Processing Theory |
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| The cognitive revolution that occurred in the 1960’s was based on classical computational logic, and the connectionist/neural network movements of the 1970’s were based on classical dynamical systems. These classical assumptions remain at the heart of both cognitive architecture and neural network theories, and they are so commonly and widely applied that they are just taken for granted and presumed to be obviously true. What are these critical but hidden assumptions upon which all traditional theories rely? Quantum information processing theory provides a fundamentally different approach to logic, reasoning, probabilistic inference, and dynamical systems. For example, quantum logic does not follow the distributive axiom of Boolean logic; quantum probabilities do not obey the Kolmogorov law of total probability; quantum reasoning does not obey the principle of monotonic reasoning. Nevertheless Mother Nature seems to rely heavily on quantum computing principles in many domains of science. This talk will provide an exposition of the basic assumptions of classic versus quantum information processing theories. | These basic assumptions will be examined, side by side, in a parallel and elementary manner. For example, classical systems assume that measurement merely observes a pre existing property of a system; in contrast, quantum systems assume that measurement actively creates the existence of a property in a system. The logic and mathematical foundation of classic and quantum theory will be laid out in a simple and elementary manner that uncovers the mysteries of both theories. Classic theory will emerge to be seen as a possibly overly restrictive case of the more general quantum theory. The fundamental implications of these contrasting assumptions will be examined closely with concrete examples and applications to cognition. New research programs in cognition based on quantum information processing theory will be reviewed. Quantum computing theory (Nielsen & Chuang, 2000) provides universal computing capabilities, but it also provides an ideal way of operating under uncertainty. In this theory, sequences of inferences and actions are accomplished by using sequences of control U gates, which are unitary operators operating on superposed quantum states. | ||||||||||||||||||||||||||||||||
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